Related papers: A large deviations principle for the Maki-Thompson…

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

Hidden stochastic effects acting uniformly on a many-particle system can generate strong correlations and macroscopic relative fluctuations that persist at large system sizes, even when the particles themselves remain causally independent.…

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…

We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…

We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…

We propose an SIS competition model describing the propagation of conflicting rumors, such as fake news and its corrections. This simple model captures the interaction between rumor propagation and opinion dynamics, where rumors drive…

Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the…

We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

We present a large deviation property for the pattern statistics representing the number of occurrences of a symbol in words of given length generated at random according to a rational stochastic model. The result is obtained assuming that…

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…

The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this…

Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…

Given a finite typed rooted tree $T$ with $n$ vertices, the {\em empirical subtree measure} is the uniform measure on the $n$ typed subtrees of $T$ formed by taking all descendants of a single vertex. We prove a large deviation principle in…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…